Understanding the Movement of a Unique Clock

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Homework Help Overview

The discussion revolves around understanding the movement and angular displacement of the hands of a unique clock. Participants are exploring whether this clock functions like a traditional clock and how the angular displacement between hour markings is defined.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants question the nature of the clock and whether it accurately represents time like a conventional clock. They inquire about the angular displacement of the clock hands and whether this displacement remains constant over time intervals.

Discussion Status

Some participants have provided assumptions regarding the clock's functionality, suggesting that the hour and minute markings can be treated as exact for the purpose of the problem. Others are exploring the relationship between angular displacement in this clock compared to a standard circular clock, raising questions about the applicability of certain angles and geometric representations.

Contextual Notes

There are references to specific angles formed by the clock hands at various positions, and discussions about the implications of these angles in relation to a traditional clock setup. The conversation includes considerations of how to visualize the problem geometrically, with suggestions to draw triangles and possibly a round clock for clarity.

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Homework Statement


see attachment
Time.PNG


Homework Equations



θ= ω*τ

The Attempt at a Solution



Nothing. Instead I have some queries about the question itself :
1.Is this a proper clock, will it show the correct time as any normal clock ?
2.what is the angular displacement of one of the clock hand when it moves from 1 to 2.
Is this angular displacement constant every 5 minutes (ie from 1 to 2 , 2 to 3 , 3 to 4 etc ).
 
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hms.tech said:

Homework Statement


see attachment
View attachment 54960

Homework Equations



θ= ω*τ

The Attempt at a Solution



Nothing. Instead I have some queries about the question itself :
1.Is this a proper clock, will it show the correct time as any normal clock ?
2.what is the angular displacement of one of the clock hand when it moves from 1 to 2.
Is this angular displacement constant every 5 minutes (ie from 1 to 2 , 2 to 3 , 3 to 4 etc ).

1. For the purposes of this question, you may assume that the *hour* will be shown exactly on the hour, ditto with the minutes in multiples of five. The interpolations between markings may not be exact, but you needn't concern yourself with this.

2. What would this be in a "regular" circular clock? Would you expect it to be different here?

3. Why wouldn't it be?
 
Curious3141 said:
1. For the purposes of this question, you may assume that the *hour* will be shown exactly on the hour, ditto with the minutes in multiples of five. The interpolations between markings may not be exact, but you needn't concern yourself with this.

2. What would this be in a "regular" circular clock? Would you expect it to be different here?

3. Why wouldn't it be?

we'll consider the time in seconds for easiness.

w= ∏/30 rad per second

More help required ...
 
When a hand points to 12, it forms an angle with the vertical of 0°.
When a hand points to 1, it forms an angle with the vertical of ??°[/size][/color]
When a hand points to 2, it forms an angle with the vertical of ??°[/size][/color]
 
NascentOxygen said:
When a hand points to 12, it forms an angle with the vertical of 0°.
When a hand points to 1, it forms an angle with the vertical of ??°[/size]
When a hand points to 2, it forms an angle with the vertical of ??°[/size]


When it points to one, it forms an angle of ∏/6
When it points to two, it forms and angle with the vertical of ∏/3
 
So you can now on the clock face draw some triangles showing lengths and angles, for a hand pointing to 1, and also for it pointing to 2.
 
NascentOxygen said:
So you can now on the clock face draw some triangles showing lengths and angles, for a hand pointing to 1, and also for it pointing to 2.

Aren't these angles only applicable to a normal "round clock" ?
 
Each hand moves at a constant angular rotation, like an ordinary clock, we are told.
 
hms.tech said:
Aren't these angles only applicable to a normal "round clock" ?

Draw a round clock in the same picture centered between 6 and 12 and extend the radii.
 
  • #10
hms.tech said:
Aren't these angles only applicable to a normal "round clock" ?

These angles are applicable to this clock, because you're told the hands move like a normal (round) clock.

You might find it easier to visualise the problem if you express everything in degrees. Consider the hand at position "n" and then at position "n+2" (two markings apart). What's the angle between those two positions?

Do you see a special triangle here? This makes things quite easy, along with some very simple trig.

You could take up LCKurtz's suggestion to draw a round clock, but personally, I think it might complicate things if you clutter the figure with a circle. I would suggest just drawing the rectangle and the various triangles within it and treating the problem as simple geometry and trig.
 

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